Edge preserving smoothing method

ABSTRACT

A method of smoothing data to reduce or remove noise while preserving edge information in the data selects an output point in the data, identifies the most homogeneous neighborhood around the selected output point and outputs a corrected value for the selected output point based upon data points in the identified neighborhood.

FIELD OF THE INVENTION

[0001] This invention relates to a method for processing noisy signalsprior to edge detection analysis.

BACKGROUND OF THE INVENTION

[0002] Suppressing random noise is an important pre-processing step inthe analysis of many signals. One area in which this pre-processing isimportant is in the analysis of seismic signals, where the suppressionof random noise is advantageously implemented prior to applying aninformation-extraction algorithm such as a seismic edge detection orcoherence cube algorithm. This pre-processing is valuable because theseismic data generally includes reflection data from around faults-andfractures in the ground, and this reflection data is usually morecomplicated and weaker than the data from other areas due to dispersion,diffraction and other forms of scattering.

[0003] Typically, prediction error filtering (PEF or f-x deconvolution)is used to precondition the data before edge detection. Prediction errorfiltering has been very successful in many areas. However, if the signalbeing pre-processed is not highly predictable, such as in areas of faultor fracture, this method is inadequate to remove the noise.

[0004] A simple alternative method is to smooth the data within movingwindows. Unlike the PEF method, this smoothing method does not stronglydepend on the predictability of the signals. The drawback here is thatthis method tends to blur the sharp edges that are associated with thefaults and channels that are intended to be enhanced in seismic edgedetection.

SUMMARY OF THE INVENTION

[0005] It is therefore an object of the present invention to provide anedge preserving smoothing method that avoids the above-describeddifficulties of the prior art.

[0006] It is a further object of the present invention to provide anedge preserving smoothing method that resolves the conflict betweennoise reduction and edge degradation, so that noise is suppressed whilesharp edges are kept intact.

[0007] The above and other objects are achieved by the present inventionwhich, in one embodiment, is directed to a method for smoothing datacomprising the steps of.

[0008] In accordance with an advantageous aspect of the presentinvention, the method can be one-, two- or three-dimensional.

[0009] These and other objects, features and advantages of the presentinvention will be apparent from the following detailed description ofthe preferred embodiments taken in conjunction with the followingdrawings, wherein like reference numerals denote like elements.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010]FIG. 1A shows a one-dimensional step function.

[0011]FIG. 1B shows the step function of FIG. 1A with added noise.

[0012]FIG. 1C shows the noisy step function of FIG. 1B after beingprocessed with a conventional smoothing method.

[0013]FIG. 1D shows the noisy step function of FIG. 1B after beingprocessed with the an embodiment of the edge-preserving smoothing methodin accordance with the present invention.

[0014]FIG. 2A illustrates the result of applying an edge-detectionalgorithm to seismic data without first applying the smoothing method inaccordance with the present invention.

[0015]FIG. 2B illustrates the result of applying the edge-detectionalgorithm to the seismic data after first applying the smoothing methodin accordance with the present invention.

[0016]FIG. 3A illustrates the result of applying the edge-detectionalgorithm to other seismic data without first applying the smoothingmethod in accordance with the present invention.

[0017]FIG. 3B illustrates the result of applying the edge-detectionalgorithm to the other seismic data after first applying the smoothingmethod in accordance with the present invention.

[0018]FIG. 4 is a flowchart of a method in accordance with the presentinvention.

[0019]FIG. 5 is a sketch of an apparatus for implementing a method inaccordance with the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] In concept, the method of the present invention looks for themost homogeneous neighborhood around each output point in a 3D seismiccube, and then give each point the average value of the selectedneighborhood.

[0021] FIGS. 1A-1D illustrate this concept using a simpleone-dimensional (1-D) step function. FIG. 1A displays a noise-free stepfunction. FIG. 1B shows the same step function after random noise isadded. Applying a conventional 21-point smoothing filter to FIG. 1Byields the result shown in FIG. 1C. It will be seen that the randomnoise has been reduced, but at the same time the sharp step has beenseverely altered.

[0022]FIG. 1D illustrates the result of applying a 21-point smoothingoperator in accordance with the present invention to FIG. 1B. In FIG.1D, it is clear that the sharp edge has been preserved while the noisehas been reduced.

[0023] While the smoothing operator in accordance with the presentinvention can be implemented for any desired number of points, for thepurpose of simplicity and clarity in the following discussion, a fivepoint smoothing operator will be described.

[0024] In this case, for any given output location, i.e. a sample pointA_(i) at the ith location, the smoothing operator calculates thestandard deviations for the following five shifted windows:

[0025] (A_(i−4) A_(i−3) A_(i−3) A_(i−1) A_(i+0))

[0026] (A_(i−3) A_(i−2) A_(i−1) A_(i+0) A_(i+1))

[0027] (A_(i−2) A_(i−1) A_(i+0) A_(i+1) A_(i+2))

[0028] (A_(i−1) A_(i+0) A_(i+1) A_(i+2) A_(i+3))

[0029] (A_(i+0) A_(i+1) A_(i+2) A_(i+3) A_(i+4))

[0030] Here A_(i) represents the amplitude of the ith sample of thenoise-added step function (FIG. 1B).

[0031] Next, the method selects the window having the minimum standarddeviation and outputs the average over this selected window as acorrected value for the ith sample of output. Repeating this process forall the output locations yields the result shown in FIG. 1D. It will beseen that the results of FIG. 1D are superior to those of FIG. 1C inpreserving the shape of the step function while removing the noise.

[0032] More generally, for an n-point window, the n windows are definedas: $\begin{matrix}\left( A_{i - n + 1} \right. & A_{i - n + 2} & \cdots & A_{i - 1} & \left. A_{i + 0} \right) \\\left( A_{i - n + 2} \right. & A_{i - n + 3} & \cdots & A_{i + 0} & \left. A_{i + 1} \right) \\\vdots & \vdots & \quad & \vdots & \vdots \\\left( A_{i + 0} \right. & A_{i + 1} & \cdots & A_{i + n - 1} & \left. A_{i + n} \right)\end{matrix}$

[0033] While the above embodiment uses a 1-D window, the method can begeneralized to two-dimensional (2-D) and three-dimensional (3-D) cases.Thus, for an output location (x₀, y₀), its vicinity space is dividedinto small fragments and the standard deviation for each fragment iscalculated separately. The fragment corresponding to the smalleststandard deviation is selected and its average value is used as theoutput for the location (x₀, y₀).

[0034] The edge-preserving smoothing method in accordance with thepresent invention can be tested by applying an edge-detection algorithmto seismic data with and without the smoothing method applied. For thistest, all the parameters for edge detection were kept the same for bothruns, so that any differences are solely attributable to the smoothingalgorithm.

[0035]FIG. 2A shows the edge-detection result using data without thesmoothing method applied, while FIG. 2B shows the result using data towhich the smoothing method was first applied. The edges in FIG. 2B areclearer and sharper than those in FIG. 2A.

[0036]FIGS. 3A and 3B illustrate another example. Here again, FIG. 3Ashows the edge-detection result using data without the smoothing methodapplied, while FIG. 3B shows the result using data to which thesmoothing method was first applied. In FIG. 3A, strong footprints arevisible, while in FIG. 3B they have been suppressed by smoothing.

[0037]FIG. 4 is a flowchart of a preferred embodiment of theedge-preserving smoothing method in accordance with the presentinvention. In step S1, the basic window parameters are defined (e.g. 1,2 or 3 dimensions, number of points, shape of the windows, slidingdistance etc.). In step S2, many windows are formed around an outputlocation and each window covers a segment of the neighborhoodsurrounding the location. In step S3 the standard deviations for thedifferent window positions around this location are calculated. In stepS4, the window having the smallest standard deviation is selected andthe average of the data in this window is output as a corrected valuefor this location. The method then returns to step S2 to completeprocessing the rest of the data.

[0038]FIG. 5 illustrates a computer 100 as an apparatus for implementingthe method in accordance with the present invention. Generally, acomputer is understood by those of ordinary skill in the art asincluding means for performing the functional steps of the method, suchas means for selecting an output point in the data, means foridentifying a most homogeneous neighborhood around the selected outputpoint, and means for outputting a corrected value for the selectedoutput point based upon data points in the identified neighborhood,where the means for identifying includes, for example, means fordefining a plurality of neighborhoods around the selected output point,means for calculating a standard deviation of data points within each ofthe plurality of neighborhoods, and means for identifying the mosthomogeneous neighborhood as the one of the plurality of neighborhoodshaving the least standard deviation.

[0039] However, those of ordinary skill in the art will understand thatother apparatus, or combinations of apparatuses, may be used to effectthese functions.

[0040] Thus, unlike the conventional f-x deconvolution or PEF methods,the method in accordance with the present invention does not heavilydepend on the predictability of signals. The edge-preserving smoothingmethod in accordance with the present invention can reduce random noisewithout altering sharp boundaries, and therefore is an idealpre-conditioning process before the application of seismicedged-detection (or coherence cube) algorithms.

[0041] While the disclosed method and apparatus have been particularlyshown and described with respect to the preferred embodiments, it isunderstood by those skilled in the art that various modifications inform and detail may be made therein without departing from the scope andspirit of the invention. Accordingly, modifications such as thosesuggested above, but not limited thereto are to be considered within thescope of the invention, which is to be determined by reference to theappended claims.

We claim:
 1. A method of smoothing data to reduce or remove noise whilepreserving edge information in the data, said method comprising thesteps of: selecting an output point in the data; identifying a mosthomogeneous neighborhood around the selected output point; andoutputting a corrected value for the selected output point based upondata in the identified neighborhood.
 2. The method of claim 1, whereinsaid identifying step identifies the most homogeneous neighborhood basedupon a standard deviation of that neighborhood.
 3. The method of claim2, wherein said identifying step includes the steps of: defining aplurality of neighborhoods around the selected output point; calculatinga standard deviation of data points within each of the plurality ofneighborhoods; and identifying the most homogeneous neighborhood as theone of the plurality of neighborhoods having the least standarddeviation.
 4. The method of claim 4, wherein each of the plurality ofneighborhoods is defined as a fragment of a 3-D seismic cube.
 5. Themethod of claim 4, wherein each of the plurality of neighborhoods isdefined by a location in the data and a window around that location. 6.The method of claim 1, wherein said identifying step includes the stepsof: defining a window; and sliding the window to a plurality ofdifferent locations around the selected output point, wherein eachposition of the window defines a respective one of a plurality ofneighborhoods; and choosing one of the plurality of neighborhoods as themost homogeneous neighborhood.
 7. The method of claim 6, wherein saidchoosing step chooses the most homogeneous neighborhood based upon astandard deviation of that neighborhood.
 8. The method of claim 7,wherein said choosing step includes the steps of: calculating a standarddeviation of data points within each of the plurality of neighborhoods;and identifying the most homogeneous neighborhood as the one of theplurality of neighborhoods having the least standard deviation.
 9. Themethod of claim 1, wherein said identifying step includes the steps of:defining a window as including a plurality n of data points; sliding thewindow to a plurality of positions around the selected output point,wherein each position of the window defines a respective one of aplurality of neighborhoods; and choosing one of the plurality ofneighborhoods as the most homogeneous neighborhood.
 10. The method ofclaim 9, wherein said choosing step chooses the most homogeneousneighborhood based upon a standard deviation of that neighborhood. 11.The method of claim 10, wherein said choosing step includes the stepsof: calculating a standard deviation of data points within each of theplurality of neighborhoods; and identifying the most homogeneousneighborhood as the one of the plurality of neighborhoods having theleast standard deviation.
 12. The method of claim 9, wherein the windowis a one-dimensional window.
 13. The method of claim 12, wherein an ithdata point is denoted A_(i), where i is an integer, wherein the npositions of the window are defined as each including one of thefollowing groups of data points: $\begin{matrix}\left( A_{i - n + 1} \right. & A_{i - n + 2} & \cdots & A_{i - 1} & \left. A_{i + 0} \right) \\\left( A_{i - n + 2} \right. & A_{i - n + 3} & \cdots & A_{i + 0} & \left. A_{i + 1} \right) \\\vdots & \vdots & \quad & \vdots & \vdots \\\left( A_{i + 0} \right. & A_{i + 1} & \cdots & A_{i + n - 1} & \left. A_{i + n} \right)\end{matrix}$

and wherein said choosing step includes the steps of: calculating astandard deviation of the data points within each of the windows; andidentifying the most homogeneous neighborhood as the one of the windowpositions having the least standard deviation.
 14. Apparatus forsmoothing data to reduce or remove noise while preserving edgeinformation in the data, said apparatus comprising: means for selectingan output point in the data; means for identifying a most homogeneousneighborhood around the selected output point; and means for outputtinga corrected value for the selected output point based upon data pointsin the identified neighborhood.
 15. The apparatus of claim 14, whereinsaid means for identifying includes: means for defining a plurality ofneighborhoods around the selected output point; means for calculating astandard deviation of data points within each of the plurality ofneighborhoods; and means for identifying the most homogeneousneighborhood as the one of the plurality of neighborhoods having theleast standard deviation.
 16. The method of claim 15, wherein each ofthe plurality of neighborhoods is defined by a location in the data anda window around that location.